A firm has sales of $10 million, variable costs of $4 million ✓ Solved

A firm has sales of $10 million, variable costs of $4 million, fixed expenses of $1.5 million, interest costs of $2 million, and a 30 percent average tax rate. a. Compute its DOL, DFL, and DCL. b. What will be the expected level of EBIT and net income if next year's sales rise 10 percent? c. What will be the expected level of EBIT and net income if next year's sales fall 20 percent?

Paper For Above Instructions

The given scenario involves assessing a firm with defined financial parameters to calculate its Degree of Operating Leverage (DOL), Degree of Financial Leverage (DFL), and Degree of Combined Leverage (DCL). Let’s begin by calculating these metrics one by one, based on the provided information.

1. Calculation of DOL, DFL, and DCL

First, we need to define the terms and calculate the respective values:

  • Sales (S): $10,000,000

  • Variable Costs (VC): $4,000,000

  • Fixed Expenses (FC): $1,500,000

  • Interest Costs (I): $2,000,000

  • Tax Rate: 30%

Calculation of DOL: The formula for Degree of Operating Leverage is:

DOL = (S - VC) / (S - VC - FC)

Substituting the values:

DOL = (10,000,000 - 4,000,000) / (10,000,000 - 4,000,000 - 1,500,000)

DOL = 6,000,000 / 4,500,000

DOL ≈ 1.33

Calculation of DFL: The formula for Degree of Financial Leverage is:

DFL = EBIT / (EBIT - I)

To compute DFL, we first need to find EBIT.

EBIT (Earnings Before Interest and Taxes) = Sales - Variable Costs - Fixed Costs

EBIT = 10,000,000 - 4,000,000 - 1,500,000 = 4,500,000

Now substituting for DFL:

DFL = 4,500,000 / (4,500,000 - 2,000,000) = 4,500,000 / 2,500,000

DFL = 1.8

Calculation of DCL: The Degree of Combined Leverage is calculated as:

DCL = DOL * DFL

DCL = 1.33 * 1.8 ≈ 2.4

2. Expected Level of EBIT and Net Income with Sales Rise of 10%

If next year's sales rise by 10%, the new sales figure will be:

New Sales = 10,000,000 * 1.10 = 11,000,000

We will compute the expected EBIT:

New EBIT = New Sales - Variable Costs - Fixed Costs

The variable costs will also rise by 10% (as they are directly proportional to sales):

New Variable Costs = 4,000,000 * 1.10 = 4,400,000

Now calculating new EBIT:

New EBIT = 11,000,000 - 4,400,000 - 1,500,000 = 5,100,000

Next, we find the net income. The interest costs remain the same at $2,000,000:

New Earnings Before Tax (EBT) = New EBIT - Interest Costs = 5,100,000 - 2,000,000 = 3,100,000

Net Income = EBT (1 - Tax Rate) = 3,100,000 (1 - 0.30) = 3,100,000 * 0.70 = 2,170,000

3. Expected Level of EBIT and Net Income with a 20% Drop in Sales

If next year's sales fall by 20%, new sales figure will be:

New Sales = 10,000,000 * 0.80 = 8,000,000

Again, variable costs will decrease in line with sales:

New Variable Costs = 4,000,000 * 0.80 = 3,200,000

Now calculating the new EBIT:

New EBIT = New Sales - New Variable Costs - Fixed Costs = 8,000,000 - 3,200,000 - 1,500,000 = 3,300,000

Subsequently, we compute the net income:

New Earnings Before Tax (EBT) = 3,300,000 - 2,000,000 = 1,300,000

Net Income = 1,300,000 (1 - 0.30) = 1,300,000 0.70 = 910,000

Conclusion

Through the calculations performed, we determine key metrics such as DOL, DFL, and DCL, which are 1.33, 1.8, and 2.4 respectively. Furthermore, we predict that if sales increase by 10%, EBIT will rise to $5,100,000 and net income will be $2,170,000. Conversely, if sales decrease by 20%, EBIT will fall to $3,300,000, leading to a net income of $910,000. Understanding these leverage metrics allows management to make informed decisions to optimize the company's capital structure and operational efficiency.

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